WASHINGTON — It soon could cost 49 cents to mail a letter. The postal Board of Governors said Wednesday it wants to raise the price of a first-class stamp by 3 cents, citing the agency’s “precarious financial condition” and the uncertain prospects for postal overhaul legislation in Congress. “Of the options currently available to the Postal Service to align costs and revenues, increasing postage prices is a last resort that reflects extreme financial challenges,” board chairman Mickey Barnett wrote customers. The rate proposal must be approved by the independent Postal Regulatory Commission. If the commission accepts it, the increase would become effective Jan. 26. Under federal law the post office cannot raise its prices more than the rate of inflation unless it gets approval from the commission. In seeking the increase, Barnett cited “extraordinary and exceptional circumstances which have contributed to continued financial losses” by the agency. As part of the rate increase request, the cost for each additional ounce of first-class mail would increase a penny to 21 cents while the price of mailing a postcard would rise by a cent, to 34 cents. The cost to mail a letter to an international destination would jump 5 cents to $1.15.